A simple analytic model is proposed which predicts the unsaturated hydraulic conductivity curves by using the moisture content-capillary head curve and the measured value of the hydraulic conductivity at saturation. It is similar to the Childs and Collis-George (1950) model but uses a modified assumption concerning the hydraulic conductivity of the pore sequence in order to take into account the effect of the larger pore section. A computational method is derived for the determination of the residual water content and for the extrapolation of the water content-capillary head curve as measured in a limited range. The proposed model is compared with the existing practical models of Averjanov (1950), Wyllie and Gardner (1958), and Millington and Quirk (1961) on the basis of the measured data of 45 soils. It seems that the new model is in better agreement with observations.

A new model for predicting the hydraulic conductivity of unsaturated porous media

This paper reviews the importance of large continuous openings (macropores) on water flow in soils. The presence of macropores may lead to spatial concentrations of water flow through unsaturated soil that will not be described well by a Darcy approach to flow through porous media. This has important implications for the rapid movement of solutes and pollutants through soils. Difficulties in defining what constitutes a macropore and the limitations of current nomenclature are reviewed. The influence of macropores on infiltration and subsurface storm flow is discussed on the basis of both experimental evidence and theoretical studies. The limitations of models that treat macropores and matrix porosity as separate flow domains is stressed. Little-understood areas are discussed as promising lines for future research. In particular, there is a need for a coherent theory of flow through structured soils that would make the macropore domain concept redundant.

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Macropores and water flow in soils

A method is presented for developing probability density functions for parameters of soil moisture relationships of capillary head [h(θ)] and hydraulic conductivity [K(θ)]. These soil moisture parameters are required for the assessment of water flow and solute transport in unsaturated media. The method employs a statistical multiple regression equation proposed in the literature for estimating [h(θ)] or [K(θ)] relationships using the soil saturated water content and the percentages of sand and clay. In the absence of known statistical distributions for either [h(θ)] or [K(θ)] relationships, the method facilitates modeling by providing variability estimates that can be used to examine the uncertainty associated with water flow or solute transport in unsaturated media.

Developing joint probability distributions of soil water retention characteristics

Hydrologic analyses often involve the evaluation of soil water infiltration, conductivity, storage, and plant-water relationships. To define the hydrologic soil water effects requires estimating soil water characteristics for water potential and hydraulic conductivity using soil variables such as texture, organic matter (OM), and structure. Field or laboratory measurements are difficult, costly, and often impractical for many hydrologic analyses. Statistical correlations between soil texture, soil water potential, and hydraulic conductivity can provide estimates sufficiently accurate for many analyses and decisions. This study developed new soil water characteristic equations from the currently available USDA soil database using only the readily available variables of soil texture and OM. These equations are similar to those previously reported by Saxton et al. but include more variables and application range. They were combined with previously reported relationships for tensions and conductivities and the effects of density, gravel, and salinity to form a comprehensive predictive system of soil water characteristics for agricultural water management and hydrologic analyses. Verification was performed using independent data sets for a wide range of soil textures. The predictive system was programmed for a graphical computerized model to provide easy application and rapid solutions and is available at http://hydrolab.arsusda. gov/soilwater/Index.htm.

/pdf/soil-water-characteristic-estimates-by-texture-and-organic-56ntsbkyo4.pdf

Soil Water Characteristic Estimates by Texture and Organic Matter for Hydrologic Solutions

Changing ideas in hydrology — The case of physically-based models

Infiltration and redistribution of water following an irrigation was studied, and
 the work was replicated at 20 locations on a 150 hectare plot of land. Hydraulic conductivity
 was measured as a function of soil-water content at 30.5 cm depth intervals to a depth
 of 182.9 in twenty 6.5-meter-square plots randomly established over a 150-hectare
 field. Tensiometers installed at 30.5, 61.0, 91.4, 121.9, 152.4, and 182.9 cm were
 used to measure hydraulic gradients. Soil-water contents were ascertained from soil-water
 characteristics obtained from six soil cores taken from each of the above depths for
 each plot. Variations in soil-water content were found to be normally distributed
 with depth and with horizontal distance throughout the field, while values of the
 hydraulic conductivity were found to be log-normally distributed. The correlation
 between hydraulic conductivity during steady-state infiltration and the clay fraction
 was significant at the 1 per cent level. Several equations for predicting water movement
 and retention under field conditions are examined.

/pdf/spatial-variability-of-field-measured-soil-water-properties-nvuvnm14w8.pdf

Spatial variability of field-measured soil-water properties

On describing and predicting the hydraulic properties of unsaturated soils

In agronomic problems the sampling procedure may create some confusion and bias in
 the analysis. Geostatistics provides a method for the analysis of the spatial and
 temporal properties in a data set and a method of interpolation between selected points.
 This paper describes the theory of geostatistics and its application to selected agronomic
 problems. Geostatistics considers a set of data collected in either space or time
 at discrete intervals. These samples may be correlated with each other to provide
 some unique information about the parameters which would not be detected in the classical
 statistical methods. Through the application of geostatistics to this type of problem,
 we can estimate the spatial or temporal dependence of samples and from this knowledge
 arrive at an estimation of the sampling procedures or structure at a field. The application
 of these techniques is shown for air temperature, surface temperature, yield, clay
 content, and fertilizer content in various fields and reveals the versatility of the
 techniques.
 Geostatistics also allows for the evaluation of the dependence between two parameters
 in either time or space. From this information it is possible to develop sampling
 procedures which would allow the more costly or time consuming variable to be sampled
 less frequently and estimated from the other variable by the method of kriging. This
 report summarizes all of these techniques and provides several different examples
 of their utilization. Examples of the computer code are provided for the reader wishing
 to apply these techniques.

Geostatistical theory and application to variability of some agronomical properties

Solute distributions within a soil profile during the leaching of water-soluble salts applied to the soil surface were measured at six depths to 182.4 cm within 20 subplots of a 150-ha field. Estimates of the pore water velocity based upon measures of solute displacement within each subplot and the entire field were found to be logarithmically normally distributed and in agreement with volumetric measures of water infiltration rates. Such agreement was only possible because it was recognized that the observed values were not normally distributed, and their mean values were calculated accordingly. The number of observations required to yield an estimate of the mean pore water velocity within a prescribed accuracy is shown to depend upon the nature and extent of the spatial variability of the field soil. For the field examined, 100 observations would allow the mean pore water velocity to be estimated within ±50% of its true value. The functional relation between field-measured values of the apparent diffusion coefficient, also found to be logarithmically normally distributed, and pore water velocity is examined and interpreted in terms of solute distributions likely to be measured at specific sampling sites.

Spatial variability of the leaching characteristics of a field soil

Accurate estimates of the unsaturated hydraulic properties are needed for any quantitative description of multiphase flow in porous media. This paper presents a consistent set of parametric models for the isothermal, hysteretic unsaturated fluid phase content (retention) and hydraulic conductivity functions of typical two-phase systems like water and air, or water and hydrocarbons. The equations are obtained by combining expressions for the hysteretic fluid retention curves with the statistical pore size distribution model of Mualem (1976) which predicts the hydraulic conductivity from more easily measured fluid retention data. Hysteresis is described using the model of Scott et al. (1983). The existence of residual fluid saturations for both the wetting and non wetting fluids is justified. Theoretical and experimental considerations indicate a need to match predicted and observed hydraulic conductivities at fluid phase contents less than full saturation.

Donald R. Nielsen

Papers

Spatial variability of field-measured soil-water properties

On describing and predicting the hydraulic properties of unsaturated soils

Geostatistical theory and application to variability of some agronomical properties

Spatial variability of the leaching characteristics of a field soil

A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface